With the age of what's there, and the layout, you should be planning a full gut remodel.

Use your lower cabinets for long-term storage so you don't have to bend down as much. If you need more room, there is an easier option than gutting your kitchen. Move your bar cart / table in the next room and have a large, floor-to-ceiling storage unit built there to accommodate some more of your day-to-day foods and dishes.

Any cabinet professional can come add some shims to higher the lower cabinet's height.
Also, there needs to be an 18' clearance from counter height to upper cabinets, so maybe taking out those open shelvings to accommodate this and lowering the high upper cabinets to the 18' clearance...
All in all, you will not have to replace any cabinets if you find someone that can do that.

That is a little strange... 2" is a substantial difference even if they laminated over the floor twice with new flooring that is substantial...

At first we were thinking they had used Universal Design/ADA compliant cabinets... but, the toe kicks are pretty much hidden and that defeats the purpose for ADA cabinets...

This would be a very uncomfortable kitchen to work in with this type of height difference unless you were used to it for some time and or smaller in height...

The cabinets are a little older looking... it might be a good idea to think about replacing them... regardless if they were built in place or piece by piece raising them will be a labor intensive... face frames screwed to face frame, walls screwed, tops popped for leveling and shimming cabinets, possibly adjusting electrical and plumbing... Basically to raise these cabinets you will have to remove them first...

Let us know if you need any further assistance or have any questions...

Not on topic...just wanna say I love your colors! Black, white, and blue! :)

it seems like even with new cabinets you will still need to raise the floor and those cabinets look like they were built in place least expensive remove counter install buil up of two inches and reinstall counter and trim out do it yourself for around $450 or get new cabinets raise the floor and spend $7 to 15 thousand

Simple, increase the height of the toe kick to raise the height of the cabinets & apply new toe kick cover. 6" is a Euro toe space height. You will have to build a platform for the dishwasher. This doesn't work if you have a range. Box in the oven cabinet toe space.
By using this method, you can change back if you sell the house.

Here is an article that might help!
http://bit.ly/1qqdy8b